The invention concerns a method for obtaining amplitude and phase dependencies of radio frequency pulses which are irradiated within the scope of a main magnetic resonance experiment for generating a predetermined n-dimensional spatial distribution (n>=1) of transverse magnetization in an object by means of at least one radio frequency transmitting antenna of a magnetic resonance measuring system in combination with spatially and temporally varying additional magnetic fields which are superimposed on the static and homogeneous base field of the magnetic resonance measuring system and change the transverse magnetization phase in the object in dependence on location and time.
A method of this type is disclosed e.g. in [9].
Magnetic resonance imaging (MRI), also called magnetic resonance tomography (MRT), is a widely used technology for non-invasive generation of images of the inside of an object under investigation and is based on the position-resolved measurement of magnetic resonance signals from the object under investigation. The object under investigation is subjected to a substantially static and homogeneous magnetic base field within a base field magnet, and for this reason, the nuclear spins within the object under investigation are oriented with respect to the direction of the base field, which is generally selected to be the z direction of a magnet-bound coordinate system. The associated orientation of the magnetic dipoles of the nuclei causes magnetization of the object in the direction of the main magnetic field, which is called longitudinal magnetization. In the MR investigation (MR: magnetic resonance), this longitudinal magnetization of the object under investigation is excited to perform a precession motion by irradiating electromagnetic RF pulses (RF: radio frequency) by means of one or more RF transmitting antennas, the frequency of the precession motion being proportional to the local magnetic field strength. The magnetization vector is thereby deflected out of the equilibrium state (z direction) through an angle, referred to below as the deflection angle. In the MRI methods that are generally used today, localized encoding, generally called spatial encoding, is impressed on the precession motions of the nuclear spins through time-varying superpositions of additional magnetic fields for all three spatial directions. The so-called gradient fields Gx, Gy and Gz which are used for this purpose and normally have constant gradients in the spatial directions x, y, and z, are generated by a coil arrangement, which is called a gradient system and is driven by a so-called gradient channel for each spatial direction. The terms linear and non-linear gradient or magnetic fields used below always refer to the spatial dependence of the fields unless another definition is given. The spatial encoding is normally described by a scheme in so-called k-space, which is conjugated from physical space via a Fourier transformation. Switching of gradient pulses in this k-space formalism, which can only be applied when magnetic fields with spatially constant gradients are used, can be described as passage through a trajectory in k-space, the so-called k-space trajectory.
The transverse component of the precessing magnetization connected with the nuclear spins, also called transverse magnetization below, induces voltage signals, also called magnetic resonance signals (MR signals), in one or more RF receiving antennas that surround the object under investigation. Time-varying magnetic resonance signals are generated by means of pulse sequences which contain specially selected series of RF pulses and gradient pulses (short-term application of temporally constant or varying gradient fields) in such a fashion that they can be converted into corresponding spatial images. This is realized in accordance with one of many well-known reconstruction technologies when the MR signals have been recorded, amplified, and digitized by means of an electronic receiving system, and processed by means of an electronic computer system, and also stored in one-dimensional or multi-dimensional datasets. The pulse sequence that is used typically contains a sequence of measuring processes in which the gradient pulses are varied in accordance with the selected localization method.
One essential precondition for spatially accurate imaging of the nuclear spins of the object under investigation is that the technical imperfections of the MR measuring system can be neglected or the deviations from ideal behavior are known and can be correspondingly corrected.
Spatially selective excitation is a technology that is widely used in magnetic resonance imaging for spatially delimiting the transverse magnetization that is generated during excitation and/or spatially varying its amplitude and phase in the excitation volume in accordance with predetermined distributions. For slice selection, which is the most frequent case of spatial selective excitation, the excitation volume is reduced to a predetermined slice. Multi-dimensional spatially selective excitation, in which the excitation volume is delimited in more than one direction and/or the excitation is modulated in more than one direction, has also produced numerous applications. These include excitation of a small three-dimensional volume within a substantially larger object under investigation for localized spectroscopy, imaging of a selectively excited region (ROI: region of interest) with reduced field of view (FOV) with the aim of reducing the measuring time or improving the resolution, excitation of special volumes that are adjusted to the structures of the object under investigation or also echo-planar imaging with reduced echo train lengths. The amplitude and phase modulation of transverse magnetization can also be used during excitation to compensate for disadvantageous effects of an inhomogeneous magnetic transmission field (B1 field) of the RF antennas used for excitation. This is an application that has become immensely important these days due to the strong increase in high field MRI systems which often involve inhomogeneities of this type.
Spatially selective excitation was conventionally performed by means of one single RF transmitting antenna with a substantially homogeneous transmission field (B1 field) in combination with the gradient system. Inspired by the success of parallel imaging, in which the signals are recorded with an arrangement of several RF receiving antennas, which is also called an antenna array in technical literature and which consists of several individual antennas or elements, one has started in the meantime to also use such antenna arrays, which consist of several elements and are operated on several RF transmission channels of the MR measuring system, for transmission with selective excitation. It is thereby possible to partially replace spatial encoding, which is realized for selective excitation analogously to acquisition by variation of gradient fields, by so-called sensitivity encoding and thereby reduce the length of the excitation pulses. One thereby utilizes the information which is contained in the different spatial variations of the transmission fields of the individual array elements (also called transmission profiles below). Since the length of such selective excitation pulses was in most cases one of the limiting criteria for the applicability of this technology, the so-called parallel excitation (PEX) or multi-channel excitation is a promising approach to use spatially selective excitation on an even wider basis than before. Spatial encoding during the transmission of RF pulses for selective excitation is called transmission spatial encoding below in order to distinguish it from spatial encoding during acquisition.
One of the basic tasks in connection with the use of selective excitation is the determination of the RF pulses that must be irradiated by the RF transmission system of the MR measuring system in order to generate the desired distribution of transverse magnetization in combination with additional magnetic fields. In the article “A k-space analysis of small tip-angle excitation” [1] Pauly et al. describe a method for single-channel spatially selective excitation by means of which the searched pulse form B1(t) can be calculated on the basis of a mathematical analogy between selective excitation and Fourier imaging substantially by Fourier transformation of the desired transverse magnetization distribution and scanning of the Fourier transform along a predetermined k-space trajectory. Katscher et al. extended this calculation method for the case of an antenna array having several independent transmission channels [2].
An object often contains several nuclear spin species having different precession frequencies, as is the case for nuclei of different chemical elements or similar nuclei in different chemical environments. The nuclear spin species can be combined into nuclear spin ensembles of the same Larmor frequency which each contribute to the overall transverse magnetization. Since the RF pulses determined according to Pauly et al. or Katscher et al. are, in general, optimum with respect to the realization accuracy of the desired transverse magnetisation distribution only for nuclear spins that precess at a determined frequency, these RF pulses excite different, generally unintentional distributions for transverse magnetization contributions of the individual nuclear spin ensembles. For this reason, Meyer et al. [3] or Setsompop [4] present e.g. methods that also allow spatially selective excitation for nuclear spin ensembles with a selected precession frequency. This case is called spatially spectrally selective excitation using spatially spectrally selective RF pulses. This approach also allows to predetermine individual distributions, which may be different or identical, for the transverse magnetization contributions of the individual nuclear spin ensembles, and excite them with one or several RF pulses. The terms spatially selective excitation or selective excitation are also used below unless the spectral selectivity is to be particularly emphasized.
The basis for the calculation methods of the RF pulses used for selective excitation are, in general, the well-known Bloch equations for describing the development of the magnetization in an object under the influence of external magnetic fields. Restricting to the case in which external fields deflect the sample magnetization out of the equilibrium state (z direction) through small angles only (called the small tip angle approximation below), the distribution of the transverse magnetization in the x-y plane, described as a complex variable, can be calculated according to the following equation (thereby neglecting relaxation effects):
                                          M            xy                    ⁡                      (            x            )                          =                  ⅈγ          ⁢                                          ⁢                      M            0                    ⁢                                    ∑              n              N                        ⁢                                                            S                  n                                ⁡                                  (                  x                  )                                            ⁢                                                ∫                  0                  T                                ⁢                                                                            B                                              1                        ,                        n                                                              ⁡                                          (                      t                      )                                                        ⁢                                      ⅇ                                          ⅈφ                      ⁡                                              (                                                  x                          ,                          t                                                )                                                                              ⁢                                      ⅆ                    t                                                                                                          (        1        )            
Mxy is the generated transverse magnetization distribution, x designates the spatial coordinate, γ defines the gyromagnetic ratio of the investigated spin species, M0 is the equilibrium magnetization (the magnetic base field is oriented in the z direction), B1,n is the RF pulse supplied to the transmitting antenna n by N, Sn is the spatial variation of the transmission field of array element n, φ is the phase that accumulates in the transverse magnetization from the time of generation to termination of the influence of the additional magnetic fields, and T is the duration of the longest one of the N RF pulses. Mxy and B1,n are complex variables, the real and imaginary parts of which describe the x or y components of the respective vector size in the coordinate system that rotates with the RF pulses (vectorial variables are in bold print).
In addition to the target pattern Mxy to be excited, a k-space trajectory knom(t), which determines, in the k-space formalism with φ(x,t)=xk(t), the time- and spatially dependent development of the phase of transverse magnetization, abbreviated below as (spatial) phase development, is predetermined and inserted in equation (1) in the calculation methods of Pauly et al. and Katscher et al. The spatial phase development thereby describes the change of the transverse magnetization phase due to the gradient fields used for k-space trajectory generation. The solution of the inverse problem with respect to equation (1) thereby provides the desired RF pulses B1,n(t), which generate the desired distribution of transverse magnetization in case of application during exact passage of the predetermined k-space trajectory.
RF pulses calculated in this fashion generally yield a high realization accuracy of the desired transverse magnetization distribution only for small deflection angles of magnetization in the validity range of the small tip angle approximation, for which reason, they are also called small-tip-angle pulses. When the small tip angle approximation is not used and RF pulses for large deflection angles (large-tip-angle pulses) are calculated, the Bloch equations produce a non-linear system of equations, for which no analytical solutions are currently known. In order to determine RF pulses, which are suited e.g. as inversion pulses or refocusing pulses, other approximations or iterative solutions of the system of equations must therefore be used, as proposed e.g. by Xu et al. [7]. This example is based e.g. on a linear connection between the transmission field (B1) and the excitation angle achieved thereby. In correspondence with small tip angle approximation, in the present case and in most calculation methods, a phase development φ(x,t) of transverse magnetization is included in the calculation of the RF pulses. This phase development is defined in this case, in particular, by a k-space trajectory with φ(x,t)=xk(t).
Since all calculations of the RF pulses in the above-presented methods are based on a k-space trajectory, the theoretical values in the calculation step and the actual values in the experiment must essentially coincide to obtain a high realization accuracy of the desired transverse magnetization distribution: Modern MR devices can generally apply RF pulses with high accuracy with respect to amplitude and phase. The k-space trajectory can, however, considerably differ from its nominally assumed dependence, as shown below, whereby the realization accuracy of the transverse magnetization distribution can be considerably reduced in dependence on the magnitude of the deviations and the selection of the k-space trajectory. Artifacts can thereby occur.
Passage through the k-space trajectory is generally realized by application of gradient pulses with additional magnetic fields that are linear in space and superimposed on the base field of the magnetic resonance measuring system. In addition to these intentional additional magnetic fields, unintentional additional magnetic fields are also present in the experiment, which need not be spatially linear or constant in time. All deviations from the intentional fields can be combined as unintentional additional magnetic fields of this type. These are i.a. inhomogeneities and variations with time of the magnetic base field which is assumed to be homogeneous and static, which ensure that the resonance frequency of the nuclear spins at certain locations of the object under investigation or at certain times no longer corresponds to the irradiated RF frequency, i.e. off-resonances occur. Amplitude deviations and time delays of actually applied gradient pulses compared to their nominally predetermined values due to technical imperfections of the gradient system and due to physical technical interferences, such as e.g. induced eddy currents and couplings in and between the components of the magnetic resonance measuring system, also occur. The term intentional or unintentional additional magnetic fields used below also includes those cases in which the field strength of these additional fields is zero.
The development with time of the transverse magnetization phase (phase development φ(x,t)) is thereby no longer solely determined in the experiment by a predetermined nominal k-space trajectory or the intentional additional magnetic fields used for the generation thereof, but also by the mentioned unintentional magnetic fields.
In consequence of these interferences, further approaches for pulse calculation of spatially selective excitation were gradually devised. Some work [5, 6] uses the so-called “conjugate-phase” (CP) approach from image reconstruction, which takes into consideration at least effects of off-resonances that must be determined in most cases in a previous experiment, as a component of unintentional additional magnetic fields and correct them to a certain degree. These approaches for pulse calculation are nevertheless not optimum in several ways. The algorithms generally produce pulses that are suboptimal with respect to the realization accuracy of the desired transverse magnetization distribution, in particular, when undersampling takes place in the k-space trajectory or when the off-resonance influences vary greatly spatially. A more recent method for pulse calculation that was introduced by Yip et al. [8] and was generalized by Grissom et al. [9] for the multi-channel transmission case, is based on an optimization approach and improves the excitation accuracy in two ways. On the one hand, it is more robust with respect to undersampling in k-space. Moreover, consideration of off-resonance influences in pulse calculation is facilitated. It also offers the possibility of including further boundary conditions, such as the control of the integrated or also maximum RF transmitting power, into the calculation, which is important in view of SAR control (SAR: Specific Absorption Rate) or in view of technical limitations of the RF power transmitters. However, deviations of the k-space trajectory that is actually generated by the gradient system from the theoretically predetermined trajectory cannot be taken into consideration with these methods.
One approach for solving the last-mentioned problem is (see Ullmann et al. [10]), to measure in situ the actually generated k-space trajectory by means of a method according to Duyn et al. [11] in a previous experiment, and to subsequently perform pulse calculation on the basis of the experimentally determined k-space trajectory. In this fashion, the calculated RF pulses are already adjusted to deviations from the nominal k-space trajectory and can compensate for these to a certain degree. The actually passed k-space trajectory or the actually effective gradient pulses are thereby determined successively and separately for each gradient channel (single-channel measurement). Towards this end, the gradient pulse to be measured of one single gradient channel is applied while an MR signal from a slice positioned perpendicularly with respect to the respective field gradient direction at a separation d from the gradient system center, is simultaneously recorded. The experiment is subsequently repeated for a second slice at a separation -d, i.e. on the opposite side of the gradient system center, which is collectively called a two-slice measurement. The single-channel measurement is thereby necessary, since simultaneous application of gradient pulses with several gradient channels and with field gradient components parallel to the excited slice can cause the following problems: The effect of a gradient channel on a certain direction of movement in k-space and thereby separation of the individual k-space directions would be prevented or considerably aggravated, and also an additional, spatially and temporally varying phase of transverse magnetization would occur, which would falsify the subsequent phase-sensitive evaluation or render it impossible by dephasing the magnetization and thereby causing signal loss. The two-slice measurement is subsequently repeated for all gradient channels. When the individual slice positions are known, the k-space trajectory can subsequently be calculated from the phase development of the recorded MR signals, which developed under the influence of the gradient pulses. One great disadvantage of this method is, however, that, owing to the single-channel measurements, couplings of individual gradient coils, which can occur during simultaneous operation of all gradient channels, cannot be completely detected. One further disadvantage is the fact that influences of the above-mentioned unintentional non-linear additional magnetic fields can either not be detected or cannot be separated by the two-slice measurement and are then erroneously interpreted as influences by linear fields.
This is a central problem of the above-described methods. The above-mentioned methods cannot reconstruct components of additional magnetic fields, the spatial dependence of which contains higher orders than linear. Nor is it possible to consider such information in the methods for pulse calculation based on k-space trajectories. The k-space formalism is based on additional magnetic fields which have a linear spatial dependence, i.e. a field gradient that is constant in one spatial direction, and thereby a phase gradient of transverse magnetization, which is also constant in this spatial direction, and thereby generate a k-space trajectory that is globally valid for the overall object. This condition is not met by spatially non-linear magnetic fields, for which reason magnetic fields of this type, either intentional or unintentional, cannot be described in the form of a k-space trajectory and cannot be integrated in the previous pulse calculation methods. It should be noted that non-linear additional magnetic fields can occur not only in the form of unintentional components but also in the form of intentional components and be applied e.g. within the scope of the recently presented novel gradient concepts [12]. Such non-linear intentional fields can partly replace the formerly used linear gradient fields, whereby in case of selective excitation, a temporal spatially dependent, intentional phase development of transverse magnetization can be predetermined instead of the k-space trajectory.
The above-presented methods for determining and considering experimental imperfections in the RF pulse calculation, which show in the form of unintentional additional magnetic fields, are therefore not suited, in particular, when the unintentional additional magnetic fields to be compensated are spatially non-linear, or when previously intentional additional magnetic fields with non-linear dependence are required.
It is therefore the underlying purpose of the present invention to devise a method for obtaining amplitude and phase dependencies of RF pulses for single-channel or multi-channel selective excitation in a so-called main experiment, in which intentional and/or unintentional additional magnetic fields, which are applied simultaneously with the RF pulses, have spatial dependencies with non-linear components and/or temporally non-constant dependencies and in which, in particular, experimental imperfections in the form of unintentional additional magnetic fields are detected, taken into consideration, and compensated for.